R.I.P. Onkyo...

Ok... But left is left and right is right. A speaker on each side vs headphone... Still left and right. What am I missing?
I get as you walk through a "field" you get different sound profile, but the input is the same. I feel like you describe the room and acoustic difference, not the actual signal.
In acoustically dead surroundings you also hear the left loudspeaker with both your left and your right ear.
 
Bob Dylan, 1964:

Come gather 'round people
Wherever you roam
And admit that the waters
Around you have grown
And accept it that soon
You'll be drenched to the bone
If your time to you is worth savin'
And you better start swimmin'
Or you'll sink like a stone
For the times they are a-changin'

Come writers and critics
Who prophesize with your pen
And keep your eyes wide
The chance won't come again
And don't speak too soon
For the wheel's still in spin
And there's no tellin' who
That it's namin'
For the loser now
Will be later to win
For the times they are a-changin'

Come senators, congressmen
Please heed the call
Don't stand in the doorway
Don't block up the hall
For he that gets hurt
Will be he who has stalled
The battle outside ragin'
Will soon shake your windows
And rattle your walls
For the times they are a-changin'

Come mothers and fathers
Throughout the land
And don't criticize
What you can't understand
Your sons and your daughters
Are beyond your command
Your old road is rapidly agin'
Please get out of the new one
If you can't lend your hand
For the times they are a-changin'

The line it is drawn
The curse it is cast
The slow one now
Will later be fast
As the present now
Will later be past
The order is rapidly fadin'
And the first one now
Will later be last
For the times they are a-changin'
 
I once built a preamplifier including a crossfeed circuit based on Fig. 3 of https://patents.google.com/patent/US3088997A/en but wasn't impressed with the result. I never used it in practice.

Jan Didden once listened to some fancy digital crossfeed circuit with responses based on his personal head related transfer functions, the crossfeed circuit also corrected for head movements. He was very impressed.
Please check out a thread I just opened in amplifiers -> headphones systems https://www.diyaudio.com/community/threads/open-wing-headphone-crossfeed-stereo-sound.391630/

Since the ear external parts (flange, concha, meatus whatever) all play critical roles in hearing, and a person's brain compensates for the individual's own (sometimes quite distinctive) physical differences, a binaural recording that enters the ear canal straight-on can only be an approximation. Anyway, when I was a student I watched Blue Max late one night and the plane realistically circled overhead -- I wore headphones and the soundtrack was binaually recorded! Reproducing music soundstage in binaural stereo, I haven't had a chance to try.
 
Ok... But left is left and right is right. A speaker on each side vs headphone... Still left and right. What am I missing?
I get as you walk through a "field" you get different sound profile, but the input is the same. I feel like you describe the room and acoustic difference, not the actual signal.
Stereo sound is also about depth/distance and height (3D), not just L/R. If you place speakers to point axially at your two ears but enter at an angle, then adjust your position front/back slowly, you will likely hit that sweet spot where stereo soundstage with depth comes into focus. You'd know how far away a musician stands or sits not just horizontal direction. Headphones don't present depth (unless binaurally recorded to simulate head/ears), so the musicians form a line that goes through the head.

When Apple announced the "new" airpod last year, I got all excited because it claimed to present the sound as if coming from the screen in front of you. I never bought one because Apple stopped mentioning the feature.
 
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I get that. Still, it's up to the engineering. I have two ears, and if I put good speakers or headphones on axis, that's the intended program IMHO. Any room reflections etc are colouration.

I have headphones (ATH-R70x) that can place the sound field so that you can hear things in front of you and behind you, left and right, up and down. I think it's called psychoacoustics.
 
I get that. Still, it's up to the engineering. I have two ears, and if I put good speakers or headphones on axis, that's the intended program IMHO. Any room reflections etc are colouration.

I have headphones (ATH-R70x) that can place the sound field so that you can hear things in front of you and behind you, left and right, up and down. I think it's called psychoacoustics.
It's not room reflections but the listener's own head including protruding nose and directional, sound-gathering outer ear parts that differentialy affect the sound waves entering both ear canals, then altogether processed by the brain (psychoacoustics) to privide source location--an evolutionary and subconsciously learned survival instinct.

Simple experiments: simulate nose back of head with fingers; covering nose with flat hand; immediately affect back/front source location.